Physics 218 Lecture 15

1. Physics 218Lecture 15 Dr. David Toback Physics 218, Lecture XV

2. Notes • Exam Next Tuesday: • Here. Usual class time: Covering: • Exam 1 material • Chapter 3(9) • Chapter 4(1-8) • Chapter 5(1-3) • Chapter 6(1-8) • Chapter 7(1-4) • Calculus 2 • Today: Rest of Chapter 8 NOT ON EXAM Physics 218, Lecture XV

3. Overview of Chapter 8 Chapter 8 is a mish-mash of topics: The basic idea is to learn about energy so you can do a new set of problems that you can’t do using previous ideas. This means understanding: Potential Energy, Mechanical Energy and when there is Conservation of Mechanical Energy (conservative forces) Physics 218, Lecture XV

4. Today Topics: • Potential Energy, Mechanical Energy and when there is Conservation of Mechanical Energy (conservative forces). • Conservation of Energy • Conservative and non-Conservative Forces How to back and forth between types of problems In many ways this is a review for the exam Physics 218, Lecture XV

5. Physics 218, Lecture XV

6. Potential Energy • Amount of energy that could be released • Gravitation potential energy: • If you lift up a ball it has the potential to do damage. • Raise it a height h => U = mgh • Compress a spring: • Spring potential energy: U = ½kx2 • Doing External Work can change the potential energy Physics 218, Lecture XV

7. Forces & Potential Energy Another definition: Physics 218, Lecture XV

8. Mechanical Energy: Conservative Systems If there is net work on an object, it changes the kinetic energy of the object (Gravity forces a ball falling from height h to speed up. Work done.) Wnet = DK If there is a change in the potential energy, there is net work done on an object: (ball falling from height h speeds up. Work done, loss of potential energy) DUTotal = -Wnet Physics 218, Lecture XV

9. Conservation of Mechanical Energy DK + DU = 0 K2+U2 = K1+U1 E = K + U = ½mv2 + (mgy +½kx2) Physics 218, Lecture XV

10. Conservative Forces If there are only conservative forces in the problem, then there is conservation of mechanical energy • Conservative: Can go back and forth along any path and the potential energy and kinetic energy keep turning into one another • Gravity • Springs • Others • Non-Conservative: As you move along a path, the potential energy or kinetic energy is turned into heat, light, sound etc. • Friction • Others Physics 218, Lecture XV

11. Old Problems Let’s do some old problems in some new ways Physics 218, Lecture XV

12. Example with Gravity A rock is held at height h and dropped. What is the speed when it hits the ground? A rock, at any height y relative to the ground, has potential energy of U=mgy. What must be the force on the rock? Physics 218, Lecture XV

13. Law of Conservation of Energy • Even if there is friction, Energy is conserved • Friction turns the energy into heat • Total Energy = Kinetic Energy + Potential Energy + Heat + Others… • This is what is conserved • Can use “lost” mechanical energy to estimate things about friction Physics 218, Lecture XV

14. Spherical Roller Coaster A roller coaster of mass m starts at rest at height y1 and falls down the path, then back up until it hits height y2 (y1 > y2). An odometer tells us that the total scalar distance traveled is d. Assuming we don’t know anything about the friction or the path, how much work is done by friction on this path? Assuming a constant force of friction, F, between the car and the track is constant, find F. Physics 218, Lecture XV

15. Friction and Springs A block of mass m is traveling on a rough surface. It reaches a spring (spring constant k) with speed vo and compresses it by an amount X. Determine m Physics 218, Lecture XV

16. Gravitational Potential Energy If I move to outer space, does is it still true that U=mgh? What is U in outer space? Physics 218, Lecture XV

17. Escape Velocity • What happens if I throw a ball up in the air? Will it fall down? • What if I throw it up really fast? • What if I throw it up REALLY fast? • Can I throw it up so fast that it will never come down? How fast would that be? Physics 218, Lecture XV

18. Package Dropped from a Rocket Drop a package with speed V at a height r0 so far above the earth’s surface, the mgh approximation doesn’t work. Eventually, the package falls to the surface of the earth. What is the final speed of the package? Why doesn’t the answer depend on the direction of the initial velocity? Physics 218, Lecture XV

19. Exam • Tuesday, here at the regular time • 4 Problems: • Problems similar to those in the book/homework/lecture • No numbers Physics 218, Lecture XV

20. Next Thursday: • Reading: Conservation of Linear Momentum Physics 218, Lecture XV

21. Advice 1 How to prepare: • Do all the homework problems and keep doing them until they are easy! How do you know when you are ready to take the exam? • Pick the hardest problems from the lecture, examples and HW. • You are ready when you can do any of those problems without looking at ANY notes/books/examples etc. My Advice 2  Physics 218, Lecture XV

22. My Advice II: Don’t come underprepared Physics 218, Lecture XV

23. Conservative Forces • Conservative: Work doesn’t depend on the path taken • A force is conservative if the net work done by the force on an object moving around any closed path is zero • Friction is an example of a non-conservative Force Physics 218, Lecture XV

24. Law of Conservation of Energy • Even if there is friction, Energy is conserved • Friction turns the energy into heat • Total Energy = Kinetic Energy + Potential Energy + Heat + Others… • This is what is conserved Physics 218, Lecture XV

25. Power & Potential Energy Definition:Power is the rate at which work is done. • P = dw/dt • Pavg = Dw/Dt • Name the unit after James Watt • 1 Watt = 1Joule/sec • Definition: Physics 218, Lecture XV

26. Gravitational Potential Energy What is the change in potential energy as you move from one point in space to another? What is a useful coordinate axis to define the gravitational potential energy? What is the potential energy in that reference point? Physics 218, Lecture XV